Is there any day of the week when airfares are statistically the cheapest to buy?
A number of people will tell you different things, but I'll say Tuesday or Wednesday.
Now, there are two parts to this question. Firstly, what day is the cheapest to fly, and then what day is the cheapest to buy.
To fly, is generally during the week days, not Monday or Friday as people are coming back / going on trips - leisure or business. Morning/evening flights are more expensive, etc etc.
Now, the key part you're asking is when do you buy.
Firstly, NOT the weekends. It's been shown, and I've seen personally, that airline ticket prices will often rise on the weekend, then drop again on Monday. The theory being that more people shop for tickets on the weekend. Annoying, but there you go.
Now, the best day? It's going to be Tuesday or Wednesday, depending on a few factors.
Travelocity's Director of Flights, Dominique Philips, says that most airlines tend to release sales on Mondays, Tuesdays, and Wednesdays
John Morrey, vice president of retail air at Expedia says in his opinion, booking on Tuesday evenings is ideal. He notes that airlines tend to release fare sales on Tuesday mornings, and if other carriers match, they usually do so by the evening. Fare sales generally end on Fridays, and Morrey says, "In addition, when airlines raise fares, they tend to do this on a weekend, so Saturdays and Sundays [are] less attractive."
He's so emphatic about this, that he has an entire article devoted to it.
So it depends a little on what you're searching for. For upcoming weekend flights, you should probably consider booking on Wednesdays. For far-ahead (not this weekend) flights, the release times described on Tuesdays seems to be the way to go :)